The data below represent a random sample of the number of home fires started by candles for the past several years. (From the National Fire Protection Association.) Find the 99% confidence interval for the mean number of home fires started by candles each year.
5460
5900
6090
6310
7160
8440
9930
Which of the following is the Statistical Interpretation?
99% of the home fires started by candle each year is between 4785 and 9297.9.
There is a 99% chance that 4785 < µ < 9297.9 contains the true mean.
95% of the home fires started by candles each year is between 5552.2 and 8530.7.
The mean number of home fires started by candles each year is between 5552.2 and 8530.7 fires.
The mean number of home fires started by candles each year is between 4785 and 9297.9 fires.
There is a 95% chance that 5552.2 < µ < 8530.7 contains the true mean number of home fires started by candles each year.
There is a 99% chance that 4785 < µ < 9297.9 contains the true mean number of home fires started by candles each year.

Answer:

I believe its -36

Step-by-step explanation:

-36+10=-26

-26/2= -13

Answer:

-36

Step-by-step explanation:

(x+10)/2 = -13

-13 times 2= -26

-26-10= -36

check

-36+10= -26

-26/2= -13

The result of the given program AX-0002 can be summarized as follows:
- AX = 0008
- BX = 000A

Now, let's break down the steps of the program to understand how the result is obtained:

1. MOV BX, AX: This instruction moves the value of AX into BX. Since AX has the initial value of 0002, BX now becomes 0002.

2. ASHL BX: This instruction performs an arithmetic shift left operation on the value in BX. Shifting a binary number left by one position is equivalent to multiplying it by 2. So, after the shift, BX becomes 0004.

3. ADD AX, BX: This instruction adds the values of AX and BX together. Since AX is initially 0002 and BX is now 0004, the result is AX = 0006.

4. ASHL BX: Similar to the previous step, this instruction performs an arithmetic shift left on BX. After the shift, BX becomes 0008.

5. INC BX: This instruction increments the value of BX by 1. So, BX becomes 0009.

At this point, the program diverges from the previous version. The next instructions are different. Let's continue:

6. OAX-000A, BX-0003: This instruction assigns the value 000A to OAX and the value 0003 to BX. OAX is now 000A and BX is 0003.

7. OAX-0009, BX-0006: This instruction assigns the value 0009 to OAX and the value 0006 to BX. OAX is now 0009 and BX is 0006.

8. OAX-0006, BX-0009: This instruction assigns the value 0006 to OAX and the value 0009 to BX. OAX is now 0006 and BX is 0009.

9. OAX-0008, BX-000A: This instruction assigns the value 0008 to OAX and the value 000A to BX. OAX is now 0008 and BX is 000A.

10. OAX-0011: This instruction assigns the value 0011 to OAX. OAX is now 0011.

11. BX-0003: This instruction assigns the value 0003 to BX. BX is now 0003.

Therefore, the final result is AX = 0011 and BX = 0003.

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Answer:

10 percent

Step-by-step explanation:

Answer:

$1000

Step-by-step explanation:

Cost of item x sales tax percentage = total sales tax

x * (0.08) = 80

Divide both sides by 0.08

x = 1000

Answer:

Friday & Sunday

Step-by-step explanation:

Thursday: 287

Friday: 618

Saturday: 973

Sunday: 532

973 < 287 + 618 = 973 < 905

We now know this isn't true.

973 < 287 + 532 = 973 < 819

This isn't true either.

973 < 532 + 618 = 973 < 1150

This is true.  The two days with the time are Friday and Sunday.

I really hope this helps you!  Tell me if it's right or not! :D

Answer:

The answer is A on Edge

Step-by-step explanation:

The answers to the questions on how she would use the colored chips are given here:

For the first percentage

20 / 100 = x/20

= 20 * 20 = 100x

400 = 100x

divide through by 100

x = 400/100

x = 4

For the second percentage

30/100 = x/20

600 = 100x

x = 600/100

x = 6

For the last

50/100 = x/20

1000 = 100x

x = 10

The proof is that 6 + 4 + 10 still gives us 20

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Using the interquartile range, range of the middle 50% of the data obtained from the patient feedback data is given by:

a) 16.

The interquartile range is the difference between the 75th percentile of the data-set and the 25th percentile, that is, the difference between the middle value of the upper half by the middle value of the lower half. It represents the middle 50% of the values in a distribution.

Researching this problem on the internet, we have a data with IQR of 16, hence the range of the middle 50% of the data obtained from the patient feedback data is given by:

a) 16.

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Answer:

(- 1, 4 ) is a solution to the equation

Step-by-step explanation:

Substitute x = - 1 and y = 4 into the left side of the equation and if the value obtained is equal to the right side then it is a solution

Given

3x + 8y = 29, then

3(- 1) + 8(4) = - 3 + 32 = 29 = right side

Thus (- 1, 4 ) is a solution of the equation

Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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The angle between vectors a and b is 71.79° for using the Dot Product property of vectors.

The given two vectors are a = ⟨2,2,−1⟩ and b = ⟨5,−3,2⟩. We need to find the angle between vectors a and b.

Using the Dot Product property of vectors we can find the angle between vectors. The formula for the dot product of vectors is given as follows.

a . b = |a| |b| cos(θ)

where |a| and |b| are the magnitudes of vectors a and b respectively and θ is the angle between vectors a and b.

Rearranging the above equation gives,

cos(θ) = (a . b) / (|a| |b|)

Taking the dot product of vectors a and b, we get,

a . b = (2 × 5) + (2 × −3) + (−1 × 2)

= 10 − 6 − 2

= 2

Now, we need to calculate the magnitudes of vectors a and b.

The magnitude of a is,

|a| = √(2² + 2² + (-1)²)

= √9

= 3

The magnitude of b is,

|b| = √(5² + (-3)² + 2²)

= √38

cos(θ) = (a . b) / (|a| |b|)

cos(θ) = 2 / (3 × √38)

cos(θ) = 0.3271

θ = cos⁻¹(0.3271)

θ = 71.79°

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The probability of rolling an odd number or rolling a 2 on a fair six-sided die is the fraction 2/3

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes

A fair six-sided die has faces numbered 1 to 6, and there are only three numbers that are odd numbers, which are 1, 2, and 3.

so;

probability of rolling an odd number = 3/6

probability of rolling a 2 = 1/6

probability of rolling an odd number or a 2 = 3/6 + 1/6

probability of rolling an odd number or a 2 =4/6

probability of rolling an odd number or a 2 = 2/3

In conclusion, 2/3 is the resulting fraction for the probability of rolling an odd number or rolling a 2 on a fair six-sided die.

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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To make the table of 7, using the table of 4 and 3, we add the value of both table consecutively.

We have to make the table of 7, using table of 4 and 3.

As we know the table of 3 is:

3  6  9  12  15  18  21  24  27  30

As we know the table of 4 is:

4  8  12  16  20  24  28  32  36  40

To from the table of 7 using the table of 4 and 3 we add the consecutive value of both table respectively.

3 + 4    6 + 8    9 + 12    12 + 16    15 + 20    18 + 24    21 + 28    24 + 32      27 + 36    30+40

Now simplify

7    14    21    28    35    42    49    56    63    70

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The complete question is:

Math 4th 11-4: Help bunty to make the table of 7, using table of 4 and 3.

Answer:

14.598

Step-by-step explanation:

When you round that number to the nearest hundredth, you'll get 14.6. Hope this helps.

\(\huge\underline{Answer -}\)

\( \huge{\implies \: \frac{ - 2 \frac{1}{4} }{ - \frac{ 2}{3} }} \\ \\ \\ \\ \huge{\implies \: \frac{ \frac{ - 9}{4} }{ \frac{ - 2}{3} } } \\ \\ \\ \\ \huge{\implies \: - \frac{9}{4} \div (\frac{ - 2}{3} )}\)

therefore , option ( 2 ) is correct.

hope helpful -,-

Answer:

1 + 1 = 2

Step-by-step explanation:

Answer:

206 miles

Step-by-step explanation:

9 stops * 2 miles = 18 miles on the subway

add the 188 miles traveled by train

188 + 18 = 206 miles

Answer:

  305 miles

Step-by-step explanation:

You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.

Distance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.

  distance = speed · time

  total distance = speed1 · time1 + speed2 · time2

  = (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi

Dylan travelled a total of 305 miles.

d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

p=17

Step-by-step explanation:

P = 3n+2r+t -1

when n=3, r=2, and t=5?

we will just substitute for the values

p=3(3)+2(2)+5-1

p=9+4+4

p=9+8

p=17

;- The value for p is 17

award as brainliest

Answer:

x= 8

y= -5

z= 0

Step-by-step explanation:

this is the correct answer to this system of equations.

Answer:

1/5

Step-by-step explanation:

Answer:

Y Intercept; (0,-2)

X: (1,0)

Step-by-step explanation:

To find the Y intercept subsitude 0 for x and solve. Same applies to X (sub 0 for y and solve)

To find the volume of a solid, we need to know its shape and dimensions. If the solid is composed of prisms, pyramids, and cones that are right, we can use the appropriate formulas to calculate their volumes. Once we have the volumes of each individual shape, we can add them together to find the total volume of the solid.

It's important to note that when rounding the answer to two decimal places, we should look at the third decimal place and round up if it is 5 or higher. For example, if the calculated volume is 12.345, rounding to two decimal places would give us 12.35.

In summary, to find the volume of a solid composed of right prisms, pyramids, and cones, we use the appropriate formulas for each shape and add the volumes together. We then round the final answer to two decimal places, rounding up if necessary.  

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Answer:

all two are similar rectangle but instead of

that pair having measure of sides = 10.2,6.2

another rectangle = 5.2,1.2

and rectangle of sides 64,36

ans other of side 8,6

Answer:

827.2 ft

Step-by-step explanation:

We can find the height of the tower using the trigonometric function tangent.

\(\tan(x) = \dfrac{\text{opposite}}{\text{adjacent}}\)

↓ plugging in the given values

\(\tan(84.476\°) = \dfrac{h}{80}\)

↓ multiplying both sides by 80

\(80 \cdot \tan(84.476\°) = h\)

↓ evaluating using a calculator

\(\boxed{h\approx 827.2\text{ ft}}\)

Answer:

the answer is -8

Step-by-step explanation:

pls give brainliest :)

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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